Implementation and assessment of a flux limiter based wetting and drying scheme in NEMO

Wetting and drying processes in shallow water systems by surges, tides and seiches have important societal, physical and biological impacts. Operational 3D regional models are of sufficient resolution, O(1 km), that the processes of wetting and drying need to be included. Here we describe a flux limiter based approach that allows a numerical ocean model with a flux formulation of tracer advection to wet and dry. The flux limiter approach limits the outflow from a cell whose depth is below a critical value defined by the user. The limiter can be a step function or a smooth function of the water depth, the latter increases model stability and avoids rapid alternation between dry and wet states on long slopes as the critical depth is approached. Furthermore, the user may proportionally limit the baroclinic fluxes as a cell transitions from wet to dry over the course of the large baroclinic time step. The simplicity of the flux limiter approach lends itself to its application within existing numerical models without significant intrusion into the code base. In this paper the vertical coordinate is restricted to pure terrain following coordinates with no -like steps. We explore the scheme’s effectiveness, sensitivities and limitations within the 3D NEMO ocean model by assessing it using test cases of increasing complexity. It is shown to perform well in classic channel test cases and 2D parabolic test cases with analytic solutions. All test cases with initially uniform temperature and salinity preserve this initial condition throughout the wetting and drying phases. The scheme’s performance against analytical 1D dam break experiments is explored and used to interpret its performance against laboratory measurements of a 2D dam break. It is also shown to run stably for a realistic 3D regional domain of the North West European shelf and to improve some aspects of the model’s performance against tide gauges.